Here is the thesis I will argue for: that x intentionally kills y does not entail that x intended that y die.
I need a relevance principle for intentions:
(RPI) If x intends that p in an action A, then x takes the epistemic conditional probability of p on A to be higher than the epistemic conditional probability of p on some relevant alternative (such as refraining from A).
Now suppose that George is falling past Fred's balcony. Under the building there is a net spread out. George's fall is such that he is virtually certain to miss the net unless his path is modified, and it is virtually certain that he'll die if he misses the net. Fred has always wanted to kill George. It's not that Fred has wanted George dead, but Fred wanted to take revenge on George, to be the cause of George's death. Fred has a baseball bat. If he hits George on the head, George's downward path will be modified and George will land on the net. There is no other intervention within Fred's power that can stop George from hitting the ground. If Fred hits George on the head with the bat, George has a 90% chance of dying from the blow, and a 1% chance of dying from landing on the net. Fred knows all this. He hits George on the head, and George dies from the blow.
Fred has intentionally killed George. But by RPI, Fred did not intend George's death, roughly because the action of hitting George with the bat did not increase the conditional (epistemic) probability of George's death.
Clearly, Fred intended that George should die of Fred's blow. Therefore, that one can intend that George die of Fred's blow without intending that George die.
This shows that there isn't going to be any plausible entailment principle for intentions, even if entailment is going to be understood along the lines of any plausible relevant logic (for the entailment from George dying of Fred's blow to George dying had better be relevant). Interestingly, it is not even true that he who intends the conjunction intends the conjuncts. Suppose that if I do nothing, p has probability 0.7 and q has probability 0.7, but the probability of the conjunction is only 0.1. But if I perform A, then p has probability 0.6, as does q, and the conjunction of p and q has probability 0.55. I want the conjunction of p and q, and I don't care about each conjunct (maybe I get a payoff if the conjunction holds, but I get nothing for each conjunct on its own). I know all this. So I perform A. I do not intend p, since I lowered the probability of p. Likewise, I do not intend q. But I do intend their conjunction.
In particular, this implies that in the Principle of Double Effect, the condition that one not intend the evil has to be expanded. Consider this weird case. If a peanut is eaten and Fred is killed, ten innocent people are saved. If the conjunction does not hold, ten innocent people die. Double Effect advocates (like me) will not permit me to wave a magic wand that simultaneously causes Fred to die and the peanut to be eaten (maybe by Fred who is allergic to peanuts?). However, note that Fred's death is not intended here, either as an end or as a means. Only the conjunction of Fred's death and the ingestion of the peanut is intended.
The correct way to expand the condition that one not intend the evil is tricky, and what I sketch in this paper still seems to me to be the best way to go.